During this past year we have made major progress on the theoretical basis for some of the essential modeling tools for an input/output, or nonparametric, model of the hippocampus. First, we have defined the kernels of the Volterra functional power series for the case of an event input and a continuous output: the case relevant to study of the dynamics of synaptic processes. We have investigated the relationship between the Volterra kernels and the so-called "Poisson kernels" estimated using the cross-correlation approach, with the consequence that we can now specify both the system characteristics and the experimental conditions that lead to an inequality between the Poisson and Volterra kernels. Second, we have developed a new means for estimating input/output properties of neural elements using artificial (feedforward) neural networks, which shows particular promise for estimating higher order nonlinearities. We also have made considerable progress in our development of a parametric model of a glutamatergic synapse, the primary excitatory synapse in the hippocampus. The current stage of this synaptic model includes a presynaptic terminal represented by voltage-dependent calcium conductances, calcium diffusion, pumps, buffers, and importantly, the kinetics of the interaction between calcium and synaptotagmin, a molecule that plays a key role in the release process. By including the kinetics of these molecular reactions, we have, for the first time, been able to account for several fundamental phenomena involving neurotransmitter release. With the relative locations of the release sites and the receptors included in the model, we have investigated the role of spatial variables such as the degree of "alignment" between pre- and postsynaptic elements. Using this model, we can for the first time study the potential functional significance of well-documented changes in the synaptic geometry that occur as a function of the pattern of synaptic activity. One of our ultimate goals is to utilize the experimentally determined kernels as a source of constraints for parametric models of the same neural system.